Sure, you can make a smaller fire, and hide it in a number of ways- shield it, 3 sides and bottom with large rocks, with the "downsides" to the fire, then replace them where they came from, that way there's no visible fire scar, and the light is somewhat contained. It also helps to finish cooking before dark and put it out early...

But most of the disadvantages still apply. It can still be smelled a long way downwind, and it still kills your night vision after dark, and someone who's used to the woods will still spot the the remains. Open fires are just never going to be very "stealthy".

If you're intent on using natural materials to cook with, you might look into building a hobo stove. It costs nothing, and is far more efficient than an open fire for cooking anyway- and you'll use much smaller sticks etc, so it vastly reduces the chore (and signs) of accumulating firewood.

Or, if you're open to using alcohol, just google "alcohol stoves" and there are lots of new designs for lighweight, homemade versions that reportedly work very well. I guarantee you'll have a lot more time for other things using a stove. Building and tending fires takes time, and is better suited for staying in one place.